Is there a dua or special practice to do for a new home? 

In general, it is good to pray 2 rakats of voluntary prayer (or more), and then to make dua that Allah make the house a place of baraka, serenity, worship, and good.

It may be good to have a dinner once one settles in, inviting people you know there and those you are beginning to know.

The Messenger of Allah (Allah bless him and give him peace) was asked, “What is the best of faith?” He said (peace and blessings be upon him),

“Feed others, and give salams to those you know and those you do not know.” [Bukhari and Muslim]

Such hadiths are understood to mean, ‘Among the best of faith…’ as the scholars explain.

Wassalam,
Faraz Rabbani